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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': -2, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '609099356548642958', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [-1.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 259.4100010465337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [7, [1]], [13, [1, -1]], [17, [1, 1]]], 'bad_primes': [3, 7, 13, 17], 'central_character': '32487.1', 'coefficient_field': '1.1.1.1', 'conductor': 32487, 'conductor_radical': 4641, 'degree': 2, 'euler_factors': [[1, 0, 2], [1, -1], [1, 1, 5], [1], [1, -6, 11], [1, -1], [1, 1], [1, 7, 19], [1, 3, 23], [1, 7, 29], [1, 7, 31], [1, -8, 37], [1, 2, 41], [1, 9, 43], [1, 7, 47], [1, 3, 53], [1, 4, 59], [1, -6, 61], [1, 4, 67], [1, -12, 71], [1, -7, 73], [1, 9, 79], [1, -9, 83], [1, 3, 89], [1, 5, 97]], 'gamma_factors': [[], [0]], 'index': 2, 'label': '2-32487-1.1-c1-0-2', 'leading_term': '1.3127154519', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/32487/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.312715451896263, 0.8323910302497498, -0.4444372172038862, -1.94190565428397, -2.74105261087894, -2.165590496452599, -0.5467332137806697, 0.6919074368475774, 0.09131365836549617, -2.360633316758002, -4.848845692706513, -5.217664340722088, -3.100306949641124, -0.3827226929538547, 0.7784420350055199, 0.2803843978109062, -0.1049993240617139, 0.6523897752764132, 1.194252660679381, -0.3665901590701303, -3.263829428925649, -4.198924163169112, -1.410487476670173, 2.483291155907444, 3.303433563158411, 0.7030999985022266, -1.202959893963221, 0.6497427063994299, 3.996203859030903, 4.352393128554754, 1.262251258709134, -1.280576353116274, -0.7069342268500778, 0.8377877354190324, 0.4764973051437774, -0.8774924138855589, -0.6977554544820143, 0.4058317203232415, -0.1105067100990424, -1.509125702381103, -0.2286147946392798, 3.629262566484009, 4.910433708568347, 1.013841566506162, -3.291357559639393, -2.644001380953896, 0.6556641405259006, 0.4684308885207647, -3.244784518479441, -4.688467320825415, -1.981832484437105, 0.2123355154508002, -0.8827092502070899, -1.828975910482315, 0.0949096657805042, 1.869166755308441, 0.6237141662301176, -1.041081460033493, -0.2964539611781246, 0.6112186774730968, -0.4063115399632484, -0.02305437692818935, 4.162534359620601, 7.08084450267833, 3.541606261594651, -2.279246568608749, -3.097011555252268, -0.3357574205287025, -0.4172255369139357, -2.683284273791061, -1.40045565958982, 2.584577578222644, 3.112252908285087, 0.2426506131457387, -0.2814054078886107, 1.892665209247397, 1.851643505183996, -0.4269166446765598, -0.6562796378311314, 0.4610103256583931, -0.7460807656875424, -1.759544378611186, 1.993340592282328, 6.588774485602629, 5.012829508723507, -0.08355207099943028, -1.090318098702421, 1.109286850681476, 0.7330107588176197, -0.7753149077414928, 1.118131762016044, 3.390687763858441, 1.404820375135055, -1.05941416403881, 0.544806649129492, 1.975683835927803, -0.587120364748516, -1.696473847959081, 2.340563582754091, 4.985605109687467, 1.886603656121977, -0.8347500306625977, 0.7526490764702432, 1.257279544435342, -1.576256085511772, -1.993509096291739, 1.172098059281828, 1.963006792478559, -0.2951306257467476, -0.7276764860772778, 0.08875719374345714, -0.94680107431156, -0.7707242441899335, 1.991553827214254, 0.1328872514885342, -7.980123767041706, -10.91507722806302, -3.37143768061854, 3.539315106234786, 2.088720912948607, -0.5660045860176255], 'positive_zeros': ['0.4244782984772047', '1.584166516790419', '2.013056746422796', '3.297809181085232', '3.853126817021179', '4.066592950464651', '4.713820937076669', '5.583624882106934', '6.309792091182054', '6.698863244184278', '7.594384870344474', '8.098571660816901', '8.581379959638945', '9.141745559810285', '9.480814621135192', '10.01754719751421', '10.79758296917969', '11.44068880681403', '11.78902839157666', '12.69047252199211', '12.86758266197280', '13.49108926857741', '14.07049921361483', '14.54978533242510', '14.92206251538509', '15.25228941168237', '16.13951410068471', '16.79903186073488', '16.93895977095951', '17.58697659095281', '18.27574906073267', '18.53987006709123', '19.19750906020334', '19.62014356302033', '19.90490498852799'], 'prelabel': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 609099356548642958, 'z1': {'__RealLiteral__': 0, 'data': '0.4244782984772047', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.584166516790419', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.013056746422796', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 259.4100010465337, 'bad_primes': [3, 7, 13, 17], 'central_character': '1.1', 'conductor': 32487, 'conductor_radical': 4641, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, -2, -1, 0, 0, 0, 1, 0, 6, -2, 1, 0, -1, 4, -1, 0, -7, 2, 0, 0, -3, 0, -4, 0, 1, 0, -7, 0, -7, 0, 6, 0, 0, -2, 8, 0, 1, 0, -2, 0, -9, -12, -1, 0, -7, 4, 0, 0, -1, -2, -3, 0, -6, 0, -7, 0, -4, 2, 6, 0, 0, -8, -1, 0, -4, 2, -3, 0, 12, 0, 7, 0, -4, 14, 0, 0, -9, -4, 1, 0, 9, 0, 1, 0, -7, 0, -3, 0, 0, 6, -7, 0, 7, 0, -5, 0, 6, 8], 'euler11': [1, -6, 11], 'euler13': [1, -1, 0], 'euler17': [1, 1, 0], 'euler19': [1, 7, 19], 'euler2': [1, 0, 2], 'euler23': [1, 3, 23], 'euler29': [1, 7, 29], 'euler3': [1, -1, 0], 'euler31': [1, 7, 31], 'euler37': [1, -8, 37], 'euler41': [1, 2, 41], 'euler43': [1, 9, 43], 'euler47': [1, 7, 47], 'euler5': [1, 1, 5], 'euler53': [1, 3, 53], 'euler59': [1, 4, 59], 'euler61': [1, -6, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 0], 'euler71': [1, -12, 71], 'euler73': [1, -7, 73], 'euler79': [1, 9, 79], 'euler83': [1, -9, 83], 'euler89': [1, 3, 89], 'euler97': [1, 5, 97], 'euler_factors': [[1, 0, 2], [1, -1, 0], [1, 1, 5], [1, 0, 0], [1, -6, 11], [1, -1, 0], [1, 1, 0], [1, 7, 19], [1, 3, 23], [1, 7, 29], [1, 7, 31], [1, -8, 37], [1, 2, 41], [1, 9, 43], [1, 7, 47], [1, 3, 53], [1, 4, 59], [1, -6, 61], [1, 4, 67], [1, -12, 71], [1, -7, 73], [1, 9, 79], [1, -9, 83], [1, 3, 89], [1, 5, 97]], 'index': 2, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32487/h'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-32487-1.1-c1-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 609099356548642958, 'z1': {'__RealLiteral__': 0, 'data': '0.4244782984772047', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '609099356548642958', 'Lhash_array': ['609099356548642958'], 'label': '2-32487-1.1-c1-0-2', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32487/h'}